Advertisements
Advertisements
प्रश्न
A solid metallic sphere of radius 6 cm is melted and made into a solid cylinder of height 32 cm. Find the:
(i) radius of the cylinder
(ii) curved surface area of the cylinder
Take π = 3.1
उत्तर
Let the radius of the sphere in γ1 and radius of cylinder is γ2 and the height of the cylinder is h.
∴ Volume of sphere = Volume of cylinder
`4/3 pi gamma_1^3 = pi gamma _2^2 h`
`⇒ 4/3 (6)^3 = gamma_2^2 xx (32) `
`⇒ 4/3 xx (36 xx 6)/8 = gamma_2^2`
`⇒ gamma_2^2 = (12xx6)/8`
`⇒gamma_2 = 3`
Radius of the cylinder is 3.
Curved surface area 2`pi gammah`
`=2 xx 22/7 xx 3 xx32 = 6.3.428 " cm"^2`
APPEARS IN
संबंधित प्रश्न
An exhibition tent is in the form of a cylinder surmounted by a cone. The height of the tent above the ground is 85 m and height of the cylindrical part of 50 m. If the diameter of the base is 168 m, find the quantity of canvas required to make the tent. Allow 20% extra for fold and for stitching. Give your answer to the nearest m2.
A cylinder of circumference 8 cm and length 21 cm rolls without sliding for `4 1/2` seconds at the rate of 9 complete rounds per second. Find the distance travelled by the cylinder in `4 1/2` seconds.
A cylindrical vessel of height 24 cm and diameter 40 cm is full of water. Find the exact number of small cylindrical bottles, each of height 10 cm and diameter 8 cm, which can be filled with this water.
Two right circular solid cylinders have radii in the ratio 3 : 5 and heights in the ratio 2 : 3. Find the ratio between their volumes.
A glass cylinder with a diameter 20 cm has water to a height of 9 cm. A metal cube of 8 cm edge is immersed in it completely. Calculate the height by which the water will up in the cylinder. Answer correct of the nearest mm. (Take π = 3.142)
The radius of two right circular cylinder are in the ratio of 2 : 3 and their heights are in the ratio of 5: 4 calculate the ratio of their curved surface areas and also the ratio of their volumes.
If the radius of a cylinder is doubled and height is halved, the volume will be doubled.
Radius of a cylinder is r and the height is h. Find the change in the volume if the height is doubled.
A housing society consisting of 5,500 people needs 100 L of water per person per day. The cylindrical supply tank is 7 m high and has a diameter 10 m. For how many days will the water in the tank last for the society?
